The Effect Of Random Phase To Severral Types Of Dynamical Systems

Chaos control is an important branch in nonlinear science, Its application has beenpenetrated in various fields. For example, aerospace and communication fields. Atpresent, in the process of researching nonlinear systems, Chaos control or chaos anti-control are important subjects in the chaos control theory. Chaos control is refers tostabilization of the chaotic system, while chaos anti-control is mainly refers tochaotization of the non-chaotic system. In short, Whether the chaotic control or chaosanti-control, The final purpose will make the system to meet the people expecting thestate.At first, We controlled the Bonhoeffer-Van der Pol (BVP) system by the randomphase in this paper, By using largest Lyapunov exponent, Poincaré surface, phaseportrait and the tine evolution to analy the system, It showed that the system has beencontrolled well. Secondly, We joined Gauss white noise as random phase to the thin platesystem, Making use of computer numerical simulation, It revealled that the system hadtransited chaos state to stable state. Finally, for stable shape memory alloy rotor system,Two types of Gauss noise-Gauss white noise and Gauss color noise, used in this paper,as random phase peturb it, By Khasminskii spherical coordinate theory and Wedig’salgorithm. Computing the largest Lyapunov exponent showed the system is chaotic,Poincaré surface, phase portrait and the tine evolution of the system further prove theconclusion.By studying the influence of random phase for dynamical systems, Joining randomphase to the dynamics equation, it can change the state of the system, Namely randomphase not only can suppress or eliminated chaos but also induce the generation of chaosphenomena, Random phase as a kind of effective method of chaotic control, Whether intheory or in the practical application, it has some of the research significance.